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If m and n are positive integers, what is the number of factors of

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If m and n are positive integers, what is the number of factors of [#permalink]

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10 Mar 2017, 02:15
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If m and n are positive integers, what is the number of factors of $$3^m7^n$$?

A. mn+m+n
B. m-n+1
C. (m-1)(n-1)
D. (m+1)(n+1)
E. mn
[Reveal] Spoiler: OA

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Re: If m and n are positive integers, what is the number of factors of [#permalink]

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10 Mar 2017, 02:26
MathRevolution wrote:
If m and n are positive integers, what is the number of factors of $$3^m7^n$$?

A. mn+m+n
B. m-n+1
C. (m-1)(n-1)
D. (m+1)(n+1)
E. mn

I think , the question should read m and n are prime numbers then only we can get the total factors as (m+1)(n+1) giving answer as D .
Example . 10^2 === > 5^2 . 2^2 giving total factors as 9 (1, 2 , 4, 5 , 10, 20, 25, 50, and 100 ) for 100.
Math Revolution GMAT Instructor
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Re: If m and n are positive integers, what is the number of factors of [#permalink]

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12 Mar 2017, 17:48
==> The number of factors of $$3^m7^n$$ becomes (m+1)(n+1).

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Re: If m and n are positive integers, what is the number of factors of [#permalink]

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13 Mar 2017, 00:02
no of factors is given by (m+1)(n+1)
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Re: If m and n are positive integers, what is the number of factors of [#permalink]

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15 Mar 2017, 15:33
MathRevolution wrote:
If m and n are positive integers, what is the number of factors of $$3^m7^n$$?

A. mn+m+n
B. m-n+1
C. (m-1)(n-1)
D. (m+1)(n+1)
E. mn

To determine the total number of factors of a particular number, we add 1 to each exponent of the prime factors in the prime factorization of that number and multiply the resulting numbers together. For example, 12 = 2^2 * 3^1; thus 12 has (2 + 1)(1 + 1) = (3)(2) = 6 factors. Here the number is 3^m * 7^n, so it has a total of (m + 1)(n + 1) factors.

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Re: If m and n are positive integers, what is the number of factors of   [#permalink] 15 Mar 2017, 15:33
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